ALEX Classroom Resources

   View Standards     Standard(s): [SC2015] PHYS (9-12) 1 :

1 ) Investigate and analyze, based on evidence obtained through observation or experimental design, the motion of an object using both graphical and mathematical models (e.g., creating or interpreting graphs of position, velocity, and acceleration versus time graphs for one- and two-dimensional motion; solving problems using kinematic equations for the case of constant acceleration) that may include descriptors such as position, distance traveled, displacement, speed, velocity, and acceleration.

[MA2019] GEO-19 (9-12) 37 :

37. Investigate and apply relationships among inscribed angles, radii, and chords, including but not limited to: the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

[MA2019] MOD-19 (9-12) 11 :

11. Plot coordinates on a three-dimensional Cartesian coordinate system and use relationships between coordinates to solve design problems.

a. Describe the features of a three-dimensional Cartesian coordinate system and use them to graph points.

b. Graph a point in space as the vertex of a right prism drawn in the appropriate octant with edges along the x, y, and z axes.

c. Find the distance between two objects in space given the coordinates of each.

Examples: Determine whether two aircraft are flying far enough apart to be safe; find how long a zipline cable would need to be to connect two platforms at different heights on two trees.

d. Find the midpoint between two objects in space given the coordinates of each.

Example: If two asteroids in space are traveling toward each other at the same speed, find where they will collide.

Use math to determine how a robot moves, and its future positions - given the model of the robot and the equations of motion, in this 14-minute episode. The goal of this video series is to teach the basics of Robotics: the what, why, and how—with examples—and to provide take-home problems to solve.

Robots need to move, but how do they determine how far to turn the wheels to get where they want? In this lesson we explore the equations of motion for differential drive robots. We will walk through how to derive these equations as well as talk about some of the possible wheel configurations a robot could have.

   View Standards     Standard(s): [MA2015] GEO (9-12) 26 :

26 ) Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [G-C3]

[MA2019] GEO-19 (9-12) 37 :

37. Investigate and apply relationships among inscribed angles, radii, and chords, including but not limited to: the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Module 5, Topic A leads students first to Thales' theorem (an angle drawn from a diameter of a circle to a point on the circle is sure to be a right angle), then to possible converses of Thales' theorem, and finally to the general inscribed-central angle theorem. Students use this result to solve unknown-angle problems. Through this work, students construct triangles and rectangles inscribed in circles and study their properties.

   View Standards     Standard(s): [MA2015] GEO (9-12) 24 :

24 ) Prove that all circles are similar. [G-C1]

[MA2019] GEO-19 (9-12) 20 :

20. Derive and apply the formula for the length of an arc and the formula for the area of a sector.

[MA2019] GEO-19 (9-12) 37 :

37. Investigate and apply relationships among inscribed angles, radii, and chords, including but not limited to: the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Module 5, Topic B defines the measure of an arc and establishes results relating to chord lengths and the measures of the arcs they subtend. Students build on their knowledge of circles from Module 2 and prove that all circles are similar. Students develop a formula for arc length in addition to a formula for the area of a sector and practice their skills solving unknown area problems.

   View Standards     Standard(s): [MA2015] GEO (9-12) 26 :

26 ) Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [G-C3]

[MA2019] GEO-19 (9-12) 37 :

37. Investigate and apply relationships among inscribed angles, radii, and chords, including but not limited to: the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

In Module 5, Topic C, students explore geometric relations in diagrams of two secant lines, or a secant and tangent line (possibly even two tangent lines), meeting a point inside or outside of a circle. They establish the secant angle theorems and tangent-secant angle theorems. By drawing auxiliary lines, students also notice similar triangles and thereby discover relationships between lengths of line segments appearing in these diagrams.